Chiral surfaces self-assembling in one-component systems with isotropic interactions

We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to self-assembly of chiral surfaces. We demonstrate the principle on a simple chiral lattice and on a more complex lattice with chiral super-cells. In addition we show that the complex lattice has interesting melting behavior with multiple morphologically distinct phases that we argue can be qualitatively predicted from the design of the interaction.Comment: 4 pages, 4 figure

Reciprocal relativity of noninertial frames and the quaplectic group

Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring particles to have locally inertial frames on a curved position-time manifold. The problem of the absolute inertial frame for other forces remains. We look again at the transformations of frames on an extended phase space with position, time, energy and momentum degrees of freedom. Under nonrelativistic assumptions, there is an invariant symplectic metric and a line element dt^2. Under special relativistic assumptions the symplectic metric continues to be invariant but the line elements are now -dt^2+dq^2/c^2 and dp^2-de^2/c^2. Max Born conjectured that the line element should be generalized to the pseudo- orthogonal metric -dt^2+dq^2/c^2+ (1/b^2)(dp^2-de^2/c^2). The group leaving these two metrics invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is 'reciprocal' in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group. The Heisenberg group itself is the semidirect product of two translation groups. This provides the noncommutative properties of position and momentum and also time and energy that are required for the quantum mechanics that results from considering the unitary representations of the quaplectic group.Comment: Substantial revision, Publicon LaTe

On a certain class of semigroups of operators

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.Comment: 11 page

A construction of Frobenius manifolds with logarithmic poles and applications

A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.Comment: 46 page

Localization of quantum wave packets

We study the semiclassical propagation of squeezed Gau{\ss}ian states. We do so by considering the propagation theorem introduced by Combescure and Robert \cite{CR97} approximating the evolution generated by the Weyl-quantization of symbols $H$. We examine the particular case when the Hessian $H^{\prime\prime}(X_{t})$ evaluated at the corresponding solution $X_{t}$ of Hamilton's equations of motion is periodic in time. Under this assumption, we show that the width of the wave packet can remain small up to the Ehrenfest time. We also determine conditions for ``classical revivals'' in that case. More generally, we may define recurrences of the initial width. Some of these results include the case of unbounded classical motion. In the classically unstable case we recover an exponential spreading of the wave packet as in \cite{CR97}

Causes of irregularities in trends of global mean surface temperature since the late 19th century

The time series of monthly global mean surface temperature (GST) since 1891 is successfully reconstructed from known natural and anthropogenic forcing factors, including internal climate variability, using a multiple regression technique. Comparisons are made with the performance of 40 CMIP5 models in predicting GST. The relative contributions of the various forcing factors to GST changes vary in time, but most of the warming since 1891 is found to be attributable to the net influence of increasing greenhouse gases and anthropogenic aerosols. Separate statistically independent analyses are also carried out for three periods of GST slowdown (1896–1910, 1941–1975, and 1998–2013 and subperiods); two periods of strong warming (1911–1940 and 1976–1997) are also analyzed. A reduction in total incident solar radiation forcing played a significant cooling role over 2001–2010. The only serious disagreements between the reconstructions and observations occur during the Second World War, especially in the period 1944–1945, when observed near-worldwide sea surface temperatures (SSTs) may be significantly warm-biased. In contrast, reconstructions of near-worldwide SSTs were rather warmer than those observed between about 1907 and 1910. However, the generally high reconstruction accuracy shows that known external and internal forcing factors explain all the main variations in GST between 1891 and 2015, allowing for our current understanding of their uncertainties. Accordingly, no important additional factors are needed to explain the two main warming and three main slowdown periods during this epoch

Sequential measurements of conjugate observables

We present a unified treatment of sequential measurements of two conjugate observables. Our approach is to derive a mathematical structure theorem for all the relevant covariant instruments. As a consequence of this result, we show that every Weyl-Heisenberg covariant observable can be implemented as a sequential measurement of two conjugate observables. This method is applicable both in finite and infinite dimensional Hilbert spaces, therefore covering sequential spin component measurements as well as position-momentum sequential measurements.Comment: 25 page

Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space

We represent quantum observables as POVMs (normalized positive operator valued measures) and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group $G$. The value space of such observables is a transitive $G$-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference and time observables.Comment: 23 page

Designing isotropic interactions for self-assembly of complex lattices

We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of the lattice to guarantee that the desired structure is a ground state. We use the method to self-assemble complex lattices not previously achieved with isotropic potentials, such as a snub square tiling and the kagome lattice. The latter is especially interesting because it provides the crucial geometric frustration in several proposed spin liquids.Comment: 4 pages, 3 figure